Seven out of the nine Australians in action advanced to Round 2 at the London Grand Slam on Tuesday, but it was world No. 51 Ebden's 6-4, 6-3, 6-4 victory over Belgian Goffin that stole the show.
Ebden, who last reached the second round at Wimbledon in 2013, will face Frenchman Stephane Robert next.
It was a composed performance from the 19-year-old, who is rewarded with a second-round meet with Frenchman Pierre-Hugues Herbert.
This time last year, Tomic was giving one of the most bizarre news conferences seen at the All England Club, claiming he had been bored during his first-round defeat to Mischa Zverev.
Tomic, 25, would ultimately be fined $15,000 (£11,600) by the International Tennis Federation for feigning injury and was dropped by then-racket sponsor Head.
This year's version looked anything but bored as Tomic, a quarterfinalist at Wimbledon in 2011, made light work of world No. 122 Hurkacz on a roasting hot but blustery Court 12. He faces Kei Nishikori next.
"I always play well here, I just need to get into a rhythm," said Tomic, who reached the main draw as a lucky loser after he lost in the final round of qualifying in Roehampton last week. "I was sick for five days and even today I didn't feel my best, but I feel a lot better. It's not easy to be sick, but I gave it another chance."
There was no trouble for No. 17 seed Ashleigh Barty in the women's draw as she saw off Stefanie Voegele 7-5, 6-3, and No. 26 Daria Gavrilova is also through following a 6-2, 6-3 win over lucky loser Caroline Dolehide. Gavrilova had been scheduled to face Zarina Diyas in the first round but the Kazakh withdrew injured on the eve of the match.
"It's really exciting," Gavrilova said. "We were all warming up and we're sharing a fitness trainer this week -- and a physio -- and we were all like, 'OK, let's get three out of three.' And we did, so it's pretty cool."
Elsewhere, Alex Bolt lost 6-2, 6-3, 7-5 to home favourite Kyle Edmund on Centre Court in their men's singles first-round match, and James Duckworth was thwarted 7-5, 6-2, 6-0 by No. 4 seed Alexander Zverev on Court No. 2.